Simultaneous inference for misaligned multivariate functional data

We consider inference for misaligned multivariate functional data that represents the same underlying curve, but where the functional samples have systematic differences in shape. In this paper we introduce a new class of generally applicable models where warping effects are modeled through nonlinear transformation of latent Gaussian variables and systematic shape differences are modeled by Gaussian processes. To model cross-covariance between sample coordinates we introduce a class of low-dimensional cross-covariance structures suitable for modeling multivariate functional data. We present a method for doing maximum-likelihood estimation in the models and apply the method to three data sets. The first data set is from a motion tracking system where the spatial positions of a large number of body-markers are tracked in three-dimensions over time. The second data set consists of height and weight measurements for Danish boys. The third data set consists of three-dimensional spatial hand paths from a controlled obstacle-avoidance experiment. We use the developed method to estimate the cross-covariance structure, and use a classification setup to demonstrate that the method outperforms state-of-the-art methods for handling misaligned curve data.Comment: 44 pages in total including tables and figures. Additional 9 pages of supplementary material and reference

Evidence of Odderon-exchange from scaling properties of elastic scattering at TeV energies

We study the scaling properties of the differential cross section of elastic proton-proton ($pp$) and proton-antiproton ($p\bar p$) collisions at high energies. We introduce a new scaling function, that scales -- within the experimental errors -- all the ISR data on elastic $pp$ scattering from $\sqrt{s} = 23.5$ to $62.5$ GeV to the same universal curve. We explore the scaling properties of the differential cross-sections of the elastic $pp$ and $p\bar p$ collisions in a limited TeV energy range. Rescaling the TOTEM $pp$ data from $\sqrt{s} = 7$ TeV to $2.76$ and $1.96$ TeV, and comparing it to D0 $p\bar p$ data at $1.96$ TeV, our results provide an evidence for a $t$-channel Odderon exchange at TeV energies, with a significance of at least 6.26$\sigma$. We complete this work with a model-dependent evaluation of the domain of validity of the new scaling and its violations. We find that the $H(x)$ scaling is valid, model dependently, within $200$ GeV $\leq \sqrt{s} \leq$ $8$ TeV, with a $-t$ range gradually narrowing with decreasing colliding energies.Comment: Accepted in EPJ C, with typos fixed, reorganized institutions updated, Appendix A, B, C, D, E added, 60 pages, 29 figures, 13 tables, Odderon significance: 6.26 sigma, conclusions unchange

Edge Potential Functions (EPF) and Genetic Algorithms (GA) for Edge-Based Matching of Visual Objects

Edges are known to be a semantically rich representation of the contents of a digital image. Nevertheless, their use in practical applications is sometimes limited by computation and complexity constraints. In this paper, a new approach is presented that addresses the problem of matching visual objects in digital images by combining the concept of Edge Potential Functions (EPF) with a powerful matching tool based on Genetic Algorithms (GA). EPFs can be easily calculated starting from an edge map and provide a kind of attractive pattern for a matching contour, which is conveniently exploited by GAs. Several tests were performed in the framework of different image matching applications. The results achieved clearly outline the potential of the proposed method as compared to state of the art methodologies. (c) 2007 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works

Physical Constraint Finite Element Model for Medical Image Registration

Due to being derived from linear assumption, most elastic body based non-rigid image registration algorithms are facing challenges for soft tissues with complex nonlinear behavior and with large deformations. To take into account the geometric nonlinearity of soft tissues, we propose a registration algorithm on the basis of Newtonian differential equation. The material behavior of soft tissues is modeled as St. Venant-Kirchhoff elasticity, and the nonlinearity of the continuum represents the quadratic term of the deformation gradient under the Green- St.Venant strain. In our algorithm, the elastic force is formulated as the derivative of the deformation energy with respect to the nodal displacement vectors of the finite element; the external force is determined by the registration similarity gradient flow which drives the floating image deforming to the equilibrium condition. We compared our approach to three other models: 1) the conventional linear elastic finite element model (FEM); 2) the dynamic elastic FEM; 3) the robust block matching (RBM) method. The registration accuracy was measured using three similarities: MSD (Mean Square Difference), NC (Normalized Correlation) and NMI (Normalized Mutual Information), and was also measured using the mean and max distance between the ground seeds and corresponding ones after registration. We validated our method on 60 image pairs including 30 medical image pairs with artificial deformation and 30 clinical image pairs for both the chest chemotherapy treatment in different periods and brain MRI normalization. Our method achieved a distance error of 0.320±0.138 mm in x direction and 0.326±0.111 mm in y direction, MSD of 41.96±13.74, NC of 0.9958±0.0019, NMI of 1.2962±0.0114 for images with large artificial deformations; and average NC of 0.9622±0.008 and NMI of 1.2764±0.0089 for the real clinical cases. Student's t-test demonstrated that our model statistically outperformed the other methods in comparison (p-values <0.05)

Understanding ground deformation mechanisms for multi-propped excavation in soft clay

Deep excavation works are carried out to construct underground infrastructures such as deep basements, subways, and service tunnels. The execution of these deep excavation works requires the use of retaining walls and bracing systems. Inadequate support systems have always been of major concern, as excessive ground movement induced during excavation could cause damage to neighboring structures, resulting in delays, disputes, and cost overruns. To gain a better understanding of the mechanisms involved in soil excavations, centrifuge model tests of deep excavations in slightly over-consolidated soft clay have been carried out using a newly developed testing system, in which the construction sequence of a multi-propped wall for deep excavations can be simulated in flight. Deformation mechanisms are observed using Particle Image Velocimetry. Settlements of the ground surface and changes in pore water pressure are monitored during the excavation. The effects of prop stiffness, wall rigidity, and excavation geometry on the characteristics of ground deformation and soil-structure interaction are demonstrated and discussed. The use of the conservation of energy within the framework of the mobilizable strength design in calculating ground movements is validated and shown to perform satisfactorily.This is the author accepted manuscript. The final published version can be found on the publisher website at: http://www.sciencedirect.com/science/article/pii/S0038080614000286 Copyright © 2014 Japanese Geotechnical Society. Production and hosting by Elsevier B.V. All rights reserved

The facies architecture of large igneous provinces: an integrated geological and geophysical approach to the characterisation of volcanic successions in 3-D

Quantifying the facies architecture of flood volcanic provinces is important as it can be used to understand the physical volcanology and rock property variations throughout the igneous succession. This is very important to the petroleum industry exploration efforts in volcanic rifted margins as volcanic successions commonly mask geophysical images of sub-volcanic petroleum plays. This problem is known as the 'sub-basalt imaging problem' and is caused by factors including the geometrical heterogeneities and elastic velocity and density contrasts through the volcanic pile. The study of facies architecture is broken down into a series of orders of scale. These scales reflect a systematic approach to the characterisation of the facies architecture, from a centimetre through to kilometre-scale, and incorporates 3D modelling of a range of data types for constructing the 3D structure of the flood volcanic successions. A system for the characterisation of lava flow scale facies is presented termed the 'intrafacies scheme'. This may be used to assess and interpret the geological facies heterogeneities present on a 'micro-scale' and link the interpretations to geophysical rock properties. The scheme is applied to outcrop-scale case studies in the Talisker Bay area of the Skye Lava Field on the Isle of Skye, Scotland. On a lava field scale of study ('meso-scale'), the geometrical relationships of several flood basalt provinces are studied, focusing on the Skye Lava Field. This is studied in ID through to 3D, revealing that the lava field may be divided into architectural sequences based on lava flow facies interpretations. The facies evolve upwards through the volcanic succession from geometrically complex thin, olivine-basaltic compound-braided lava flow facies towards the base, to simple, thick basaltic-andesite tabular lava flows. The lower lavas are interpreted to have formed on the gently dipping flanks of a shield volcano. The observations and understanding of flood volcanics on a lava field scale of observation and the facies forming the building blocks of lava fields are used to interpret the GFA-99 2D seismic data from the Faeroe-Shetland Basin. The interpretation is developed into 3D and thicknesses of the Faeroes Lava Group are calculated. The complete study of facies from intrafacies through to basin-scale interpretations reveal that flood volcanic successions contain substantial geometrical and rock property heterogeneities, and that these can be characterised in the 3D modelling environment into geologically realistic geophysical flood basalt facies architectural models